Solved – Can F1 score be equal to zero

As it is mentioned in F1 score Wikipedia that 'F1 score reaches its best value at 1 (perfect precision and recall) and worst at 0'.

What is the worst condition that was mentioned?

Yes. As explained in this answer the F measure can be written as:

$F_{beta}=frac{(beta^2 +1)PR}{R+beta^2P}$

Then if $P$ or $R$ is zero the $F_{beta}$ would be zero, and for the $F_1$ in your case suppose that the true labels for a binary classification problem are 1, 1, 0, 0 but your predictions are 0, 0, 1, 1 both the recall and precision are 0 so the $F_1$ is also 0.

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